1 . (8 points) Assume you have a rational weak preference relation over a finite set of alternatives. Prove that the following property of the indifference relation is true for all x and y in the set of alternatives: X ~ Y = y ~ x price and powerous 2. (8 points) You are grocery shopping and see a sign for a sale on apples. Apples are buy one, get one free! As you are approaching the display, you notice a man reads the sign and picks up only one apple then heads toward the checkout line. What, if anything, does this decision indicate about the man's consumption preferences? Is his behavior consistent with traditional economic theory regarding consumer choice